Question: The equation of a circle $C$ is $x^2+y^2+8x-10y+16 = 0$. What is its center $(h, k)$ and its radius $r$ ?
To find the equation in standard form, complete the square. $(x^2+8x) + (y^2-10y) = -16$ $(x^2+8x+16) + (y^2-10y+25) = -16 + 16 + 25$ $(x+4)^{2} + (y-5)^{2} = 25 = 5^2$ Thus, $(h, k) = (-4, 5)$ and $r = 5$.